Question about British Citizen living in Florida??

Wasn't sure where to put this. So here goes. Have a few questions. Hope some one has some answers.
My brother-in-laws..daughter lives in Tampa Bay,Florida. She is 20 something and a British citizen. She has been in US for some years now. Lives with her mom who is married to an American citizen.  Daughter has a 22 month old son,by an American citizen. They are not together any more. Father did sign the birth certificate. Does not pay child support and doesn't see this child often. Daughter is wanting to move back to the UK next year with son. She has not gotten any type UK passport for this child. She is just thinking she is going to pack her bags and bring this child into the UK without any problems. The father of this baby will not sign anything saying the baby can leave the USA. So now the questions; What exactly does she need to do to bring son with her to live over here in UK? What will the father need to do for this to be possible? Will she need to get a UK passport for son..since she is a UK citizen(the baby was born in the US)? What will happen if she tries to bring this baby over here without permission from the father? She is thinking she is just going to move over here...get a job as a carer..get a council flat....raise her baby as British. Don't think it is that simple..but would like some advice. My brother-in-law
seems to think that baby can come over here on a family passport. They don't have those any more..that I know of. Appreciate any wise words of wisdom. Thanks.

She should contact the British Consulate & get the child registered as a UK citizen and get him a British passport (assuming he qualifies for British citizenship, which he most likely does).  What kind of custody arrangement does she have with the father at the moment? Is it informal or formal? best approach would be to get it formalised in the courts if she hasn't already done so, and take it from there.

They don't do family passports anymore, you're right about that.  I'm afraid I don't have any practical advice, but I will say that what your niece is planning to do is actually exactly what my MIL did with my husband back in 1982.  I'm not sure how the laws have changed, so I don't know if it's still possible, but it certainly was then.  She just packed up and got on a plane with him.

She should contact the British Consulate & get the child registered as a UK citizen and get him a British passport (assuming he qualifies for British citizenship, which he most likely does).  What kind of custody arrangement does she have with the father at the moment? Is it informal or formal? best approach would be to get it formalised in the courts if she hasn't already done so, and take it from there.

The custody arrangement is informal. Niece says father doesn't want much to do with baby. She says the courts would want a DNA test to make sure this is the father of baby which will cost £500.00...plus all the costs of a lawyer. She says she can't afford this now.
Kind of a sticky stituation.
Don't think I would up and just bring the baby over here without a formal agreement from father.
I'm not sure if she would get away with this or not.